Problem: Multiply the following complex numbers: $({2}) \cdot ({-1-3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2}) \cdot ({-1-3i}) = $ $ ({2} \cdot {-1}) + ({2} \cdot {-3}i) + ({0}i \cdot {-1}) + ({0}i \cdot {-3}i) $ Then simplify the terms: $ (-2) + (-6i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -2 + (-6 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -2 + (-6 + 0)i - 0 $ The result is simplified: $ (-2 - 0) + (-6i) = -2-6i $